Internal problem ID [11864]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{3} \left (c_{1} \sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 22
DSolve[x^2*y''[x]-5*x*y'[x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3 (c_2 \cos (\log (x))+c_1 \sin (\log (x))) \]